Republican J. Christopher Giancarlo leans on his history at the regulator, ability to reach out to Democrats as he reviews postcrisis regulations

WASHINGTON—J. Christopher Giancarlo moved to the top job at the Commodity Futures Trading Commission this year from a minority commissioner’s role, giving him a chance to push for changes on Obama-era derivatives regulations that he has criticized.

But so far, Mr. Giancarlo has been content to tweak derivatives rules tied to the 2010 Dodd-Frank regulatory-overhaul law. His assertion that the bulk of Dodd-Frank derivatives regulations is here to stay has been disarming to some Democrats, who have worried about large-scale...